共查询到20条相似文献,搜索用时 31 毫秒
1.
Nunzio Cappuccio Marco Ferrante Giovanni Fonseca 《Statistics & probability letters》1998,40(4):379-384
In the present note we study the threshold first-order bilinear model where {e(t), tεN} is a sequence of i.i.d. absolutely continuous random variables, X(0) is a given random variable and a, b1, b2 and c are real numbers. Under suitable conditions on the coefficients and lower semicontinuity of the densities of the noise sequence, we provide sufficient conditions for the existence of a stationary solution process to the present model and of its finite moments of order p. 相似文献
X(t)=aX(t−1)+(b11{X(t−1)<c}+b21{X(t−1)c})X(t−1)e(t−1)+e(t), tεN
2.
U. G. Abdullaev 《Applied Mathematics Letters》1994,7(6):85-89
We consider the nonlinear parabolic equation ut = (k(u)ux)x + b(u)x, where u = u(x, t, x ε R1, t > 0; k(u) ≥ 0, b(u) ≥ 0 are continuous functions as u ≥ 0, b (0) = 0; k, b > 0 as u > 0. At t = 0 nonnegative, continuous and bounded initial value is prescribed. The boundary condition u(0, t) = Ψ(t) is supposed to be unbounded as t → +∞. In this paper, sufficient conditions for space localization of unbounded boundary perturbations are found. For instance, we show that nonlinear equation ut = (unux)x + (uβ)x, n ≥ 0, β >; n + 1, exhibits the phenomenon of “inner boundedness,” for arbitrary unbounded boundary perturbations. 相似文献
3.
Shaul K. Bar-Lev 《Statistics & probability letters》1990,10(5):377-379
Let
be a natural exponential family on ??? with variance function (V, Ω). Here, Ω is the mean domain of
and V is its variance expressed in terms of the mean μ ε Ω. In this note we prove the following result. Consider an open interval Ω = (0, b), 0 < b ∞, and a positive real analytic function V on Ω. If V2 is absolutely monotone on [0, b) and V has the form μt(μ), where 1 and t is real analytic in a neighborhood of zero, then there exits an infinitely divisible natural exponential family with variance function (V, Ω). We illustrate this result with several examples of general nature. 相似文献
4.
Xiaoyu Hu 《Stochastic Processes and their Applications》1999,80(2):249-269
Let {X(t), 0t1} be a stochastic process whose range is a random Cantor-like set depending on an -sequence (0<<1) and μ is the occupation measure of X(t). In this paper we examine the multifractal structure of μ and obtain the fractal dimensions of the sets of points of where the local dimension of μ is different from . It is interesting to notice that the final results of this paper are identical to those for the occupation measure of a stable subordinator with index , yet the stochastic process under consideration in this work is not even a Markov process. 相似文献
5.
Francesca Biagini Yaozhong Hu Bernt
ksendal Agns Sulem 《Stochastic Processes and their Applications》2002,100(1-2):233-253
We prove a stochastic maximum principle for controlled processes X(t)=X(u)(t) of the formwhere B(H)(t) is m-dimensional fractional Brownian motion with Hurst parameter
. As an application we solve a problem about minimal variance hedging in an incomplete market driven by fractional Brownian motion. 相似文献
dX(t)=b(t,X(t),u(t)) dt+σ(t,X(t),u(t)) dB(H)(t),
6.
Set to set broadcasting in communication networks 总被引:1,自引:0,他引:1
Suppose G = (V,E) is a graph whose vertices represent people and edges represent telephone lines between pairs of people. Each person knows a unique message and is ignorant of the messages of other people at the beginning. These messages are then spread by telephone calls. In each call, two people exchange all information they have so far in exactly one unit of time. Suppose A and B are two nonempty subsets of V. The main purpose of this paper is to study the minimum number b(A,B,G) of telephone calls by which A broadcasts to B; and the minimum time t(A,B,G) such that A broadcasts to B. In particular, we give an exact formula for b(A,B,Kn) and linear-time algorithms for computing b(A,B,T) and t(A,B,T) of a tree T. 相似文献
7.
Sergei L. Bezrukov 《Discrete Applied Mathematics》2001,110(2-3):101-119
We consider embeddings of the complete t-ary trees of depth k (denotation Tk,t) as subgraphs into the hypercube of minimum dimension n. This n, denoted by dim(Tk,t), is known if max{k,t}2. First, we study the next open cases t=3 and k=3. We improve the known upper bound dim(Tk,3)2k+1 up to limk→∞dim(Tk,3)/k5/3 and show limt→∞dim(T3,t)/t=227/120. As a co-result, we present an exact formula for the dimension of arbitrary trees of depth 2, as a function of their vertex degrees. These results and new techniques provide an improvement of the known upper bound for dim(Tk,t) for arbitrary k and t. 相似文献
8.
We prove the boundedness of all solutions for the equation x" + V'(x) = DxG(x,t), where V(x) is of singular potential, i.e., limx→-1 Y(x) = ∞, and G(x, t) is bounded and periodic in t. We give sufficient conditions on V(x) and G(x, t) to ensure that all solutions are bounded. 相似文献
9.
We investigate two families of Lorenz-like three-dimensional nonlinear dynamical systems (i) the generalized Lorenz system and (ii) the Burke–Shaw system. Analytical investigation of the former system is possible under the assumption (I) which in fact concerns four different systems corresponding to = ±1, m = 0, 1. The fixed points and stability characteristics of the Lorenz system under the assumption (I) are also classified. Parametric and temporal (t → ∞) asymptotes are also studied in connection to the memory of both the systems. We calculate the Lyapunov exponents and Lyapunov dimension for the chaotic attractors in order to study the influence of the parameters of the Lorenz system on the attractors obtained not only when the assumption (I) is satisfied but also for other values of the parameters σ, r, b, ω and m. 相似文献
10.
Margaret B. Cozzens
Mark D. Halsey
《Discrete Applied Mathematics》1991,30(2-3):125-135Let the coboxicity of a graph G be denoted by cob(G), and the threshold dimension by t(G). For fixed k≥3, determining if cob(G)≥k and t(G)≤k are both NP-complete problems. We show that if G is a comparability graph, then we can determine if cob(G)≤2 in polynomial time. This result shows that it is possible to determine if the interval dimension of a poset equals 2 in polynomial time. If the clique covering number of G is 2, we show that one can determine if t(G)≤2 in polynomial time. Sufficient conditions on G are given for cob(G)≤2 and for t(G)≤2. 相似文献
11.
We first prove that if a is both left (b; c)-invertible and left (c; b)- invertible, then a is both (b; c)-invertible and (c; b)-invertible in a *-monoid, which generalizes the recent result about the inverse along an element by L. Wang and D. Mosić [Linear Multilinear Algebra, Doi.org/10.1080/03081087. 2019.1679073], under the conditions (ab)* = ab and (ac)* = ac: In addition, we consider that ba is (c; b)-invertible, and at the same time ca is (b; c)-invertible under the same conditions, which extend the related results about Moore- Penrose inverses studied by J. Chen, H. Zou, H. Zhu, and P. Patrício [Mediterr J. Math., 2017, 14: 208] to (b; c)-inverses. As applications, we obtain that under condition (a2)* = a2; a is an EP element if and only if a is one-sided core invertible, if and only if a is group invertible. 相似文献
12.
《Discrete Mathematics》1999,200(1-3):137-147
We form squares from the product of integers in a short interval [n, n + tn], where we include n in the product. If p is prime, p|n, and (2p) > n, we prove that p is the minimum tn. If no such prime exists, we prove tn √5n when n> 32. If n = p(2p − 1) and both p and 2p − 1 are primes, then tn = 3p> 3 √n/2. For n(n + u) a square > n2, we conjecture that a and b exist where n < a < b < n + u and nab is a square (except n = 8 and N = 392). Let g2(n) be minimal such that a square can be formed as the product of distinct integers from [n, g2(n)] so that no pair of consecutive integers is omitted. We prove that g2(n) 3n − 3, and list or conjecture the values of g2(n) for all n. We describe the generalization to kth powers and conjecture the values for large n. 相似文献
13.
The bondage number b(G) of a graph G is the cardinality of a minimum set of edges whose removal from G results in a graph with a domination number greater than that of G. In this paper, we obtain the exact value of the bondage number of the strong product of two paths. That is, for any two positive integers m≥2 and n≥2, b(Pm? Pn) = 7 - r(m) - r(n) if (r(m), r(n)) = (1, 1) or (3, 3), 6 - r(m) - r(n) otherwise, where r(t) is a function of positive integer t, defined as r(t) = 1 if t ≡ 1 (mod 3), r(t) = 2 if t ≡ 2 (mod 3), and r(t) = 3 if t ≡ 0 (mod 3). 相似文献
14.
In this paper we consider the variable coefficient equation ut=b(t)uux+a(t)uxx which among other applications has considerable interest in nonlinear acoustics. We present transformation properties of this generalised equation. In particular, we classify the Lie classical symmetries, the nonclassical symmetries, the potential symmetries, point and potential form preserving transformations. Finally, using these transformations we give examples of exact solutions. 相似文献
15.
Choosability conjectures and multicircuits 总被引:5,自引:0,他引:5
This paper starts with a discussion of several old and new conjectures about choosability in graphs. In particular, the list-colouring conjecture, that ch′=χ′ for every multigraph, is shown to imply that if a line graph is (a : b)-choosable, then it is (ta : tb)-choosable for every positive integer t. It is proved that ch(H2)=χ(H2) for many “small” graphs H, including inflations of all circuits (connected 2-regular graphs) with length at most 11 except possibly length 9; and that ch″(C)=χ″(C) (the total chromatic number) for various multicircuits C, mainly of even order, where a multicircuit is a multigraph whose underlying simple graph is a circuit. In consequence, it is shown that if any of the corresponding graphs H2 or T(C) is (a : b)-choosable, then it is (ta : tb)-choosable for every positive integer t. 相似文献
16.
J. H. Bagley 《Stochastic Processes and their Applications》1985,20(2):333-341
If Z (t) is the sum of the characteristics at time t of the population in a Crump-Mode-Jagers branching process, and T is the time to extinction, it is known that under certain conditions, the distribution of Z (t) conditioned on {T > t} converges to a proper distribution as t→∞. We derive necessary and sufficient conditions in terms of the offspring process, for the existence of integral moments of this limit distribution. 相似文献
17.
Jaeger (1979) proved that if a graph has two edge-disjoint spanning trees, then it is supereulerian, i.e., that it has a spanning closed trail. Catlin (1988) showed that if G is one edge short of having two edge-disjoint spanning trees, then G has a cut edge or G is supereulerian. Catlin conjectured that if a connected graph G is at most two edges short of having two edge-disjoint spanning trees, then either G is supereulerian or G can be contracted to a K2 or a K2,t for some odd integer t 1. We prove Catlin's conjecture in a more general context. Applications to spanning trails are discussed. 相似文献
18.
For a double array {V_(m,n), m ≥ 1, n ≥ 1} of independent, mean 0 random elements in a real separable Rademacher type p(1 ≤ p ≤ 2) Banach space and an increasing double array {b_(m,n), m ≥1, n ≥ 1} of positive constants, the limit law ■ and in L_p as m∨n→∞ is shown to hold if ■ This strong law of large numbers provides a complete characterization of Rademacher type p Banach spaces. Results of this form are also established when 0 p ≤ 1 where no independence or mean 0 conditions are placed on the random elements and without any geometric conditions placed on the underlying Banach space. 相似文献
19.
In the present paper, we consider the following generalization of Besicovitch functions. Let {λn} satisfy Hadamard condition, write
f(t)=∑∞n=1ancosλnt.
We are interested in the intrinsic relationship among the coefficients {an}, the modulus of continuity of f and the upper Box dimension of graph of f. Especially, constructive structure of the function f which can be deduced from the (upper) Box dimension is a very interesting subject, and is hardly ever touched upon as far as we are aware. 相似文献
20.
Tams Lengyel 《Discrete Mathematics》1996,150(1-3):281-292
We partially characterize the rational numbers x and integers n 0 for which the sum ∑k=0∞ knxk assumes integers. We prove that if ∑k=0∞ knxk is an integer for x = 1 − a/b with a, b> 0 integers and gcd(a,b) = 1, then a = 1 or 2. Partial results and conjectures are given which indicate for which b and n it is an integer if a = 2. The proof is based on lower bounds on the multiplicities of factors of the Stirling number of the second kind, S(n,k). More specifically, we obtain
for all integers k, 2 k n, and a 3, provided a is odd or divisible by 4, where va(m) denotes the exponent of the highest power of a which divides m, for m and a> 1 integers.
New identities are also derived for the Stirling numbers, e.g., we show that ∑k=02nk! S(2n, k) , for all integers n 1. 相似文献